Definition 1 [1]}
Suppose a matrix \(A \in \mathbb {R}^{m \times n}\)  of rank \(r\)  with singular value decomposition \(A = U_{A}\Sigma _{A} V_{A}^{T}\)  where \(U_{A} \in \mathbb {R}^{m \times r}\) , \(V_{A} \in \mathbb {R}^{n \times r}\)  are orthonormal and \(\Sigma _{A} \in \mathbb {R}^{r \times r}\)  is a diagonal matrix. The statistical leverage scores of \(A\)  are defined as \(\ell _{i} = \Vert (U_{A})_{i,:}\Vert _2^2, i \in [m]\) , where \((U_{A})_{i,:}\)  is the \(i\) -th row of \(U_{A}\) . The matrix coherence of \(A\)  is defined as \(c = {\rm max}_{i \in [m]}\ell _{i}\) , which is the largest statistical leverage score of \(A\) .

